A note on quaternion matrices and split quaternion matrix pencils

2017 ◽  
Vol 58 (1-2) ◽  
pp. 323-334
Author(s):  
Istkhar Ali
Keyword(s):  
Quaternion Matrix ◽  
Split Quaternion ◽  
Quaternion Matrices ◽  
Matrix Pencils ◽  
Split Quaternion Matrix

scholarly journals Matrices over hyperbolic split quaternions

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 913-920 ◽  
Author(s):  
Melek Erdoğdu ◽  
Mustafa Özdemir
Keyword(s):  
Matrix Representation ◽  
Quaternion Matrix ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Quaternion Matrices ◽  
Hyperbolic Split Quaternion ◽  
Split Quaternion Matrix

In this paper, we present some important properties of matrices over hyperbolic split quaternions. We examine hyperbolic split quaternion matrices by their split quaternion matrix representation.

Matrix pencils with symmetries: Nonstandard involution

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Canonical Forms ◽  
Quaternion Matrix ◽  
Quaternion Matrices ◽  
Matrix Pencils

This chapter involves quaternion matrix pencils or, equivalently, pairs of quaternion matrices, with symmetries with respect to a fixed nonstandard involution φ‎. Here, the chapter provides canonical forms for φ‎-hermitian pencils, i.e., pencils of the form A + tB, where A and B are both φ‎-hermitian. It also provides canonical forms for φ‎-skewhermitian pencils. The canonical forms in question are with respect to either strict equivalence of pencils or to simultaneous φ‎-congruence of matrices. Applications are made to joint φ‎-numerical ranges of two φ‎-skewhermitian matrices and to the corresponding joint φ‎-numerical cones. The chapter fixes a nonstandard involution φ‎ throughout and a quaternion β‎(φ‎) such that φ‎=(β‎(φ‎)) = −β‎(φ‎) and ∣β‎(φ‎)∣ = 1.

Mixed matrix pencils: Nonstandard involutions

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Canonical Form ◽  
The Other ◽  
Canonical Forms ◽  
Quaternion Matrix ◽  
Mixed Matrix ◽  
Quaternion Matrices ◽  
Matrix Pencils

This chapter also studies the canonical forms of mixed quaternion matrix pencils, i.e., such that one of the two matrices is φ‎-hermitian and the other is φ‎-skewhermitian, with respect to simultaneous φ‎-congruence. It starts by formulating the canonical form for φ‎-hsk matrix pencils under strict equivalence. Other canonical forms of mixed matrix pencils are developed with respect to strict equivalence. As an application, this chapter provides canonical forms of quaternion matrices under φ‎-congruence. As in the preceding chapter, this chapter also fixes a nonstandard involution φ‎ throughout and a quaternion β‎(φ‎) such that φ‎=(β‎(φ‎)) = −β‎(φ‎) and ∣β‎(φ‎)∣ = 1.

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

2015 ◽  
Vol 56 (8) ◽  
pp. 083509 ◽  
Author(s):  
Tongsong Jiang ◽  
Ziwu Jiang ◽  
Zhaozhong Zhang
Keyword(s):  
Quaternion Matrix ◽  
Split Quaternion ◽  
Split Quaternion Matrix
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